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Chordal graphs are precisely the graphs that are both odd-hole-free and even-hole-free (see holes in graph theory). Every chordal graph is a strangulated graph , a graph in which every peripheral cycle is a triangle, because peripheral cycles are a special case of induced cycles.
In the mathematical area of graph theory, an undirected graph G is strongly chordal if it is a chordal graph and every cycle of even length (≥ 6) in G has an odd chord, i.e., an edge that connects two vertices that are an odd distance (>1) apart from each other in the cycle.
Cycle graph, a graph that consists of a single cycle; Chordal graph, a graph in which every induced cycle is a triangle; Directed acyclic graph, a directed graph with no directed cycles; Forest, a cycle-free graph; Line perfect graph, a graph in which every odd cycle is a triangle; Perfect graph, a graph with no induced cycles or their ...
In mathematics, a chord diagram consists of a cyclic order on a set of objects, together with a one-to-one pairing (perfect matching) of those objects. Chord diagrams are conventionally visualized by arranging the objects in their order around a circle , and drawing the pairs of the matching as chords of the circle.
The chordal graphs are the graphs formed by a construction of this type in which, at the time a vertex is added, its neighbors form a clique. Chordal graphs may also be characterized as the graphs that have no holes (even or odd). [35] They include as special cases the forests, the interval graphs, [36] and the maximal outerplanar graphs. [37]
A triangle-free graph is a graph with no induced cycle of length three. The cographs are exactly the graphs with no induced path of length three. The chordal graphs are the graphs with no induced cycle of length four or more. The even-hole-free graphs are the graphs containing no induced cycles with an even number of vertices.
Every cycle of length at least 6 has a chord connecting two vertices that are a distance > 1 apart from each other in the cycle.. In the mathematical area of graph theory, a chordal bipartite graph is a bipartite graph B = (X,Y,E) in which every cycle of length at least 6 in B has a chord, i.e., an edge that connects two vertices that are a distance > 1 apart from each other in the cycle.
3. A strongly chordal graph is a chordal graph in which every cycle of length six or more has an odd chord. 4. A chordal bipartite graph is not chordal (unless it is a forest); it is a bipartite graph in which every cycle of six or more vertices has a chord, so the only induced cycles are 4-cycles. 5.